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Quantum Monte Carlo Simulations Of The Fermi Polaron Problem And Bosons With Gaussian Interactions
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Book Synopsis Quantum Monte Carlo Simulations of the Fermi-polaron Problem and Bosons with Gaussian Interactions by : Peter Kroiß
Download or read book Quantum Monte Carlo Simulations of the Fermi-polaron Problem and Bosons with Gaussian Interactions written by Peter Kroiß and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Monte Carlo Methods in Condensed Matter Physics by : Masuo Suzuki
Download or read book Quantum Monte Carlo Methods in Condensed Matter Physics written by Masuo Suzuki and published by World Scientific. This book was released on 1993 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews recent developments of quantum Monte Carlo methods and some remarkable applications to interacting quantum spin systems and strongly correlated electron systems. It contains twenty-two papers by thirty authors. Some of the features are as follows. The first paper gives the foundations of the standard quantum Monte Carlo method, including some recent results on higher-order decompositions of exponential operators and ordered exponentials. The second paper presents a general review of quantum Monte Carlo methods used in the present book. One of the most challenging problems in the field of quantum Monte Carlo techniques, the negative-sign problem, is also discussed and new methods proposed to partially overcome it. In addition, low-dimensional quantum spin systems are studied. Some interesting applications of quantum Monte Carlo methods to fermion systems are also presented to investigate the role of strong correlations and fluctuations of electrons and to clarify the mechanism of high-c superconductivity. Not only thermal properties but also quantum-mechanical ground-state properties have been studied by the projection technique using auxiliary fields. Further, the Haldane gap is confirmed by numerical calculations. Active researchers in the forefront of condensed matter physics as well as young graduate students who want to start learning the quantum Monte Carlo methods will find this book useful.
Book Synopsis Quantum Monte Carlo Approaches for Correlated Systems by : Federico Becca
Download or read book Quantum Monte Carlo Approaches for Correlated Systems written by Federico Becca and published by Cambridge University Press. This book was released on 2017-11-30 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to state-of-the-art quantum Monte Carlo techniques for applications in strongly-interacting systems. Including variational wave functions, stochastic samplings, the variational technique, optimisation techniques, real-time dynamics and projection methods and recent developments on the continuum space. An extensive resource for students and researchers.
Book Synopsis Quantum Monte Carlo Methods in Physics and Chemistry by : M.P. Nightingale
Download or read book Quantum Monte Carlo Methods in Physics and Chemistry written by M.P. Nightingale and published by Springer Science & Business Media. This book was released on 1998-12-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a considerable growth in interest in Monte Carlo methods, and quantum Monte Carlo methods in particlular. Clearly, the ever-increasing computational power available to researchers, has stimulated the development of improved algorithms, and almost all fields in computational physics and chemistry are affected by their applications. Here we just mention some fields that are covered in the lecture notes contained in this volume, viz. electronic structure studies of atoms, molecules and solids, nuclear structure, and low- or zero-temperature studies of strongly-correlated quantum systems, both of the continuum and lattice variety, and cooperative phenomena in classical systems. Although each area of application may have its own peculiarities, requiring specialized solutions, all share the same basic methodology. It was with the intention of bringing together researchers and students from these various areas that the NATO Advanced Study Institute on Quantum Monte Carlo Methods in Physics and Chemistry was held at Cornell University from 12 to 24 July, 1998. This book contains material presented at the Institute in a series of mini courses in quantum Monte Carlo methods. The program consisted of lectures predominantly of a pedagogical nature, and of more specialized seminars. The levels varied from introductory to advanced, and from basic methods to applications; the program was intended for an audience working towards the Ph.D. level and above. Despite the essentially pedagogic nature of the Institute, several of the lectures and seminars contained in this volume present recent developments not previously published.
Book Synopsis The Monte Carlo Method in Condensed Matter Physics by : Kurt Binder
Download or read book The Monte Carlo Method in Condensed Matter Physics written by Kurt Binder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is now widely used and commonly accepted as an important and useful tool in solid state physics and related fields. It is broadly recognized that the technique of "computer simulation" is complementary to both analytical theory and experiment, and can significantly contribute to ad vancing the understanding of various scientific problems. Widespread applications of the Monte Carlo method to various fields of the statistical mechanics of condensed matter physics have already been reviewed in two previously published books, namely Monte Carlo Methods in Statistical Physics (Topics Curro Phys. , Vol. 7, 1st edn. 1979, 2ndedn. 1986) and Applications of the Monte Carlo Method in Statistical Physics (Topics Curro Phys. , Vol. 36, 1st edn. 1984, 2nd edn. 1987). Meanwhile the field has continued its rapid growth and expansion, and applications to new fields have appeared that were not treated at all in the above two books (e. g. studies of irreversible growth phenomena, cellular automata, interfaces, and quantum problems on lattices). Also, new methodic aspects have emerged, such as aspects of efficient use of vector com puters or parallel computers, more efficient analysis of simulated systems con figurations, and methods to reduce critical slowing down at i>hase transitions. Taken together with the extensive activity in certain traditional areas of research (simulation of classical and quantum fluids, of macromolecular materials, of spin glasses and quadrupolar glasses, etc.
Book Synopsis Quantum Monte Carlo Simulations of Disordered Fermi Systems by : Carey Bryan Huscroft
Download or read book Quantum Monte Carlo Simulations of Disordered Fermi Systems written by Carey Bryan Huscroft and published by . This book was released on 1998 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Monte Carlo Methods in Quantum Problems by : M.H. Kalos
Download or read book Monte Carlo Methods in Quantum Problems written by M.H. Kalos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been a tool of theoretical and computational scientists for many years. In particular, the invention and percolation of the algorithm of Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller sparked a rapid growth of applications to classical statistical mechanics. Although proposals for treatment of quantum systems had been made even earlier, only a few serious calculations had heen carried out. Ruch calculations are generally more consuming of computer resources than for classical systems and no universal algorithm had--or indeed has yet-- emerged. However, with advances in techniques and in sheer computing power, Monte Carlo methods have been used with considerable success in treating quantum fluids and crystals, simple models of nuclear matter, and few-body nuclei. Research at several institutions suggest that they may offer a new approach to quantum chemistry, one that is independent of basis ann yet capable of chemical accuracy. That. Monte Carlo methods can attain the very great precision needed is itself a remarkable achievement. More recently, new interest in such methods has arisen in two new a~as. Particle theorists, in particular K. Wilson, have drawn attention to the rich analogy between quantum field theoty and statistical mechanics and to the merits of Monte Carlo calculations for lattice gauge theories. This has become a rapidly growing sub-field. A related development is associated with lattice problems in quantum physics, particularly with models of solid state systems. The~ is much ferment in the calculation of various one-dimensional problems such as the'Hubbard model.
Book Synopsis Recent Advances In Quantum Monte Carlo Methods - Part Ii by : William A Lester
Download or read book Recent Advances In Quantum Monte Carlo Methods - Part Ii written by William A Lester and published by World Scientific. This book was released on 2002-02-27 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book consists of 16 chapters written by some of the most notable researchers in the field of quantum Monte Carlo, highlighting the advances made since Lester Jr.'s 1997 monograph with the same title. It may be regarded as the proceedings of the Symposium on Advances in Quantum Monte Carlo Methods held during the Pacifichem meeting in December 2000, but the contributions go beyond what was presented there.
Book Synopsis Ultracold Bose and Fermi Dipolar Gases : a Quantum Monte Carlo Study by : Raúl Bombín Escudero
Download or read book Ultracold Bose and Fermi Dipolar Gases : a Quantum Monte Carlo Study written by Raúl Bombín Escudero and published by . This book was released on 2020 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of study of this thesis are dipolar systems in the quantum degenerate regime. In general, dealing with many-body systems and evaluating their properties requires to deal with the the Schrödinger equation. In the present study we employ different Monte Carlo methods that allow to find numerical solutions to it by employing a set of stochastic techniques. The simplest one that we introduce corresponds to the Variational Monte Carlo (VMC) method, that despite its simplicity, allows to obtain variational solutions to the many-body problem. A more accurate description is provided by Diffusion Monte Carlo (DMC), that provides exact solutions for the ground state of the system when dealing with bosons. We continue presenting two methods that rely on the Feynman's path integral formalism of quantum mechanics: Path Integral Monte Carlo (PIMC) and Path Integral Ground State (PIGS), that provide exact solutions for the bosonic problem at finite and zero temperature respectively. In order to work with fermionic systems, as we do in chapter 4 of this thesis, the DMC algorithm has to be modified with the Fixed-Node (FN) approximation, what alows to avoid the sign problem. Doing so, the results obtained with DMC correspond to variational upper bounds to the energy.In chapter 3 we study the superfluid properties of a system of dipolar bosons that are fully polarized and in which the atoms are restricted to move in the plane. We also consider that all the dipolar moments form a certain tilting angle with the axis perpendicular to the plane, what allows to introduce anisotropy in the system. The phase diagram at zero temperature of this system reveals the existence of three different phases: gas, stripe and solid. Here we focus on the characterization of the superfluid properties across that phase diagram. Our calculations allow to address the question of whether the stripe phase of this system could be a candidate for the supersolid, a system that simultaneously exhibit spatial long-range order and superfluidity. By the employment of DMC and PIGS, we report finite supefluid and condensate fractions, both in the gas and the stripe phases. Then, the study is completed by performing finite temperature calculations, where the use of PIMC allows to characterize the BKT transition and to report the critical temperature at which it occurs in the different phases. Finally, by direct comparison with the predictions of the Luttinger Liquid theory, we explicitly show that the stripe phase can not be described as an ensemble of 1D isolated systems.In chapter 4, we study the fermionic dipolar system in two dimensions, focusing in the case in which all dipoles are polarized along the direction, that in this case is chosen to be the one perpendicular to the plane containing their movement. We compute the equation of state of the system in a wide range of interaction parameters. In the low density regime, the comparison of our results for the dipolar model with those of a hard-disks one allows to determine the regime of universality. On the other hand, at higher densities ( and before crystallization), we discuss the issue of itinerant ferromagnetism, that is, the possibility of having a polarized phase as the ground state of the system. The repulsive Fermi polaron with dipolar interaction, that corresponds to the limit of ultralow concentration of impurities embebed in a fermionic bath is also studied. Here we determine the regime of universality for this problem and compute observables that allow to discuss the validity of the quasi-particle picture.In the last part of the thesis, the formation of ultra-dilute dipolar droplets is studied. Our results are in agreement with experimental measurements performed with dysprosium atoms. On the other hand, the evaluation of their differences with the prediction of the extended Gross-Pitaevskii equation makes it possible to determine the limits of the mean-field approach to this problem.
Book Synopsis An Introduction to Quantum Monte Carlo Methods by : Tao Pang
Download or read book An Introduction to Quantum Monte Carlo Methods written by Tao Pang and published by Morgan & Claypool Publishers. This book was released on 2016-12-07 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been very prominent in computer simulation of various systems in physics, chemistry, biology, and materials science. This book focuses on the discussion and path-integral quantum Monte Carlo methods in many-body physics and provides a concise but complete introduction to the Metropolis algorithm and its applications in these two techniques. To explore the schemes in clarity, several quantum many-body systems are analysed and studied in detail. The book includes exercises to help digest the materials covered. It can be used as a tutorial to learn the discussion and path-integral Monte Carlo or a recipe for developing new research in the reader's own area. Two complete Java programs, one for the discussion Monte Carlo of 4^He clusters on a graphite surface and the other for the path-integral Monte Carlo of cold atoms in a potential trap, are ready for download and adoption.
Book Synopsis Quantum Monte Carlo Simulations for Disordered Bose Systems by :
Download or read book Quantum Monte Carlo Simulations for Disordered Bose Systems written by and published by . This book was released on 1992 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interacting bosons in a random potential can be used to model 3He adsorbed in porous media, universal aspects of the superconductor-insulator transition in disordered films, and vortices in disordered type II superconductors. We study a model of bosons on a 2D square lattice with a random potential of strength V and on-site repulsion U. We first describe the path integral Monte Carlo algorithm used to simulate this system. The 2D quantum problem (at T=0) gets mapped onto a classical problem of strings or directed polymers moving in 3D with each string representing the world line of a boson. We discuss efficient ways of sampling the polymer configurations as well as the permutations between the bosons. We calculate the superfluid density and the excitation spectrum. Using these results we distinguish between a superfluid, a localized or Bose glass'' insulator with gapless excitations and a Mott insulator with a finite gap to excitations (found only at commensurate densities). We discover novel effects arising from the interpaly between V and U and present preliminary results for the phase diagram at incommensurate and commensurate densities.
Book Synopsis Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems by : Masuo Suzuki
Download or read book Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems written by Masuo Suzuki and published by Springer. This book was released on 1987 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Monte Carlo Simulations of Ultracold Bosons in a Double Well by : Joel Christopher Corbo
Download or read book Quantum Monte Carlo Simulations of Ultracold Bosons in a Double Well written by Joel Christopher Corbo and published by . This book was released on 2013 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present path integral ground state (PIGS) quantum Monte Carlo calculations for the ground state (T = 0) properties of repulsively interacting bosons in a three-dimensional external double well potential over a range of interaction strengths and potential parameters. We focus our calculations on ground state number statistics and the one-body density matrix in order to understand the level of squeezing and fragmentation that the system exhibits as a function of interaction strength, and we compare our PIGS results to both a standard and an improved two-mode model and a recently-proposed eight-mode model. In general, the various models agree with the PIGS simulations for weak interactions, but the full quantum Monte Carlo treatment is required to correctly predict the amount of squeezing and fragmentation exhibited for strong interactions. One novel and somewhat surprising result from our simulations involves the relationship between squeezing and interaction strength: rather than a monotonic relationship between these quantities, we find that for certain double well barrier heights the squeezing increases as a function of interaction strength until it reaches a maximum, after which it decreases again. We also see a similar relationship between fragmentation and interaction strength. We propose novel physical mechanisms to account for this behavior.
Book Synopsis Quantum Monte Carlo Study of Strongly Interacting Fermi Gases by :
Download or read book Quantum Monte Carlo Study of Strongly Interacting Fermi Gases written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Monte Carlo Study of One-dimensional Bosons with Finite Range Interactions by : Víctor Camí Núñez
Download or read book Quantum Monte Carlo Study of One-dimensional Bosons with Finite Range Interactions written by Víctor Camí Núñez and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We have studied how the ground state and the one-body density distribution of a one-dimensional system of bosons trapped by a harmonic oscillator potential depend on the repulsive interaction between the bosons. This study has been done using two numerical methods: Variational Monte Carlo and Diffusion Monte Carlo to retrieve information about the ground state energy and the one-body density distribution. We have covered the full range of interaction from the non-interacting regime, where the mean field approximation is a suitable way to describe our system, to the strongly interacting regime where we have reproduced approximately the behavior of a Tonks-Girardeau gas. As the repulsive interaction strength is increased, the system builds pair correlations. We have also proposed a correlated wave function to characterise these correlations.
Book Synopsis Cold Atomic Fermi Gases by : Christopher Newman Gilbreth
Download or read book Cold Atomic Fermi Gases written by Christopher Newman Gilbreth and published by . This book was released on 2013 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Monte Carlo Simulations in Novel Geometries by : Vladimir Iglovikov
Download or read book Quantum Monte Carlo Simulations in Novel Geometries written by Vladimir Iglovikov and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Monte Carlo simulations are giving increasing insight into the physics of strongly interacting bosons, spins, and fermions. Initial work focused on the simplest geometries, like a 2D square lattice. Increasingly, modern research is turning to more rich structures such as honeycomb lattice of graphene, the Lieb lattice of the CuO2 planes of cuprate superconductors, the triangular lattice, and coupled layers. These new geometries possess unique features which affect the physics in profound ways, eg a vanishing density of states and relativistic dispersion ("Dirac point") of a honeycomb lattice, frustration on a triangular lattice, and a flat bands on a Lieb lattice. This thesis concerns both exploring the performance of QMC algorithms on different geometries (primarily via the "sign problem") and also applying those algorithms to several interesting open problems.
